''I hope,'' he said, ''that after this year we can let these programs (affecting poor and elderly Americans) alone - let them stabilize - for a couple of years. Let's direct our fire at some of the other programs that have escaped (spending cuts).''

Liberals agree that in fashioning the 1983 budget resolution the Republican-led Senate came down less hard on programs affecting the poor than the Democratic-controlled House, where the budget ax was sharper.

Part of the credit belongs to Senator Dole, who - as chairman of two key committees, Finance and a nutrition subcommittee - whittled down the cuts the White House originally had sought.

On food stamps, for example, the senator said, the White House had proposed a billion trim.

The aim of his nutrition subcommittee, he said, was not so much to remove people from food-stamp rolls as to reduce the ''11 percent error rate (in determining eligibility) in the states to about 5 percent over three years.''

More broadly, says Robert Greenstein, director of the Center on Budget and Policy Priorities, the 1983 budget passed by House and Senate cuts spending for domestic programs by ''about 61 percent of what President Reagan asked for.''

Domestic programs in this sense include both the ''core'' welfare programs specifically targeted to the poor and others - such as social security and medicare - that flow out to categories of Americans regardless of income.

The growth of social security outlays - the largest entitlement program and a political hot potato tossed gingerly from White House to Congress and back - was not limited by the 1983 budget.

Social security and medicare, though they swallow the bulk of all social spending - money transferred from working Americans to nonworkers - are not ''means-tested.'' Rich citizens as well as poor get benefits under these programs.

Medicare outlays would be trimmed by $13.6 billion over the 1983-85 period, according to the Senate Finance Committee's projection for the budget resolution approved by Congress.

The medicare trims - putting limits on government reimbursement to hospitals and doctors and increasing patient contributions - were made partly on the grounds that middle-class recipients can afford to pay more for their health care.

''Medicare payments,'' said Senator Dole, citing the need for spending cuts, ''are heading toward $100 billion a year in 1990. In 1965 the estimate for 1990 was $9 billion.''

The ''fairness'' issue does not arise in the case of medicare, but only in those ''core'' welfare programs aimed at needy people. These are chiefly Aid to Families with Dependent Children (AFDC), Supplementary Security Income (SSI), food stamps, child nutrition, and medicaid.

No one knows what the final budget figures in these categories will be, until separate congressional committees spell out specific spending cuts, interpreting or implementing the guidelines laid down by the 1983 budget resolution passed by Congress.

First off the mark in this process was the Senate Finance Committee. By July 20, other Senate committees are supposed to follow, with House committees working against an Aug. 1 deadline.

Over the next three years, according to the budget resolution, $8 billion will be cut from five core welfare programs - medicaid, AFDC, child nutrition, SSI, and food stamps.

Coming on top of severe trims in these programs in the current 1982 budget, many poor, elderly, and handicapped Americans will be further affected by cuts. Had the House budget version prevailed, however, the 1983-85 cuts would have totalled $17.7 billion.

The conference committee, reconciling the House and Senate budgets, adopted the less drastic Senate numbers for these five programs, on which millions of Americans at the low end of the income scale depend.

''These programs,'' notes Mr. Greenstein, ''are the same programs which sustained the largest percentage cuts last year (1982).''

Many legislators of both parties agree that mushrooming welfare costs have spiraled out of control and that program cuts are essential, first of all to eliminate waste and abuse. The problem is how to accomplish this fairly.

''When you makes cuts in programs like food stamps and medicaid,'' said Senator Dole, ''it is hard not to affect some people who do not deserve it.''